Apparatus for real-time dynamic chemical analysis

ABSTRACT

An apparatus comprising a near infrared (NIR) spectrometer and a processor with an algorithm configured to acquire NIR spectral data and perform a chemometric data manipulation provides direct measurement of the etch rate for semiconductor wafer etchant solutions. The apparatus may also provide the concentrations of species in etchant and cleaning solutions, and automated process control. The apparatus may be used for analysis and control of other processing solutions.

RELATED APPLICATION

The present application is a Divisional Application of U.S. patent application Ser. No. 10/807,537 filed 23 Mar. 2004, and claims priority to this parent application and to Israel Patent Application No. 145649 filed 25 Sep. 2001. All of these applications have the same inventors and the same assignee.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to chemical analysis of processing solutions, and more specifically to apparati for determining chemical concentrations and processing rates.

2. Description of the Related Art

In the chemical, semiconductor and biotechnological industries there are many processes that require real-time analysis and control of a reaction. Such processes involve gas-phase, liquid-phase, solid-state and mixed-phase reactions. In many cases, only indirect methods suitable for off-line use are available to analyze reactants and reaction products, so as to provide control the reaction. There is a need for methods and apparati that provide real-time analysis of reactants and reaction products, and on-line process control.

In the semiconductor industry, etching of semiconductor wafers is an important process, typically involving a thin layer of silicon oxide (or silicon nitride) on the surface of a silicon wafer. The etching process is typically performed in an aqueous etchant solution (bath) based on a hydrogen fluoride etchant. Because of the thin layers and fine circuitry features involved, the etch rate must be closely controlled to provide acceptable results with high yield. It is also important to control other semiconductor processes, such as surface preparation and cleaning processes, which often involve some mild etching.

Etching process control is typically accomplished by periodically etching test wafers for a predetermined time in the etchant solution and measuring the thickness of the wafer or etched layer before and after the etching process, coupled with additions of etchant species or water to the bath to adjust the etch rate. This approach is unsatisfactory since the test wafers are expensive, the test procedure is time consuming and labor intensive, and production from the etching process is interrupted, resulting in down time (or the use of dual etching lines). Furthermore, the test wafer approach provides no information about the etchant solution chemistry, which is typically dynamic and complex so as to render process control more difficult.

The issues involved in controlling etchant solutions are well illustrated by considering hydrofluoric acid (HF), which is the most widely used etchant for SiO₂ layers. It is generally accepted that HF dissociates in water according to the equilibria:

HF=[H⁺]+[F⁻]

HF+[F⁻]=[HF²⁻]

yielding the HF²⁻ ion. Both HF and HF²⁻ etch SiO₂ but the etch rate for HF²⁻ is 4 to 5 times greater than that for HF itself [J. S. Judge, J. Electrochem. Soc., p. 1772 (1971)]. In dilute HF solutions, HF²⁻ is much more stable then HF, the ratio [HF]/[HF²⁻] depending strongly on the pH and ionic strength of the solution.

Wet etching of SiO₂ in aqueous HF solutions is generally accepted to involve the reactions:

SiO₂+6 HF−>2 H⁺+SiF₆ ²⁻+2 H₂O

SiO₂+4 HF−>2 H⁺+SiF₄+2 H₂O

and analogous reactions for etching of SiO₂ by the HF²⁻ ion. In water, SiF₄ dissociates to give fluorosilic acid (H₂SiF₆). Fluorosilic acid and other acids with the general chemical formula Si_(i)F_(j)(OH₂)_(k) (where i+j+k=6) are the main byproducts of the SiO₂ etching process in HF solutions. It has been found that these byproducts are themselves SiO₂ etchants, with etch rates about 20 times higher than that of HF. Hence, etch rates for aged HF baths (used to process silicon wafers) tend to be higher than for freshly prepared baths. The etch rate for an aged HF bath depends on the concentrations of the various etchant species (HF, HF₂ ⁻ and fluorosilic acids), which exhibit different etch rates and are involved in complex equilibria.

From this discussion, it is clear that the wafer etch rate for aged HF etching baths changes as a function of bath usage and cannot be controlled by measuring the concentrations of H⁺ and F⁻ only. Even if the concentrations of all etchant species present in the bath are known, it is difficult to predict the etch rate due to the complex and dynamic equilibria involved. The etch rate provided by a given species may also be affected by relatively slow adsorption of another etchant species or desorption of its byproduct, or other interactions among etchant species. The situation is further complicated by “boundary layer” effects associated with transport of the various etchant species to the wafer surface from the bulk solution and transport of reaction byproducts away from the wafer surface via solution agitation and diffusion across the diffusion layer at the surface.

Wet etching systems typically involve immersion baths or spraying chambers engineered to control boundary layer phenomena and reduce their effects on the over all etch rate. Solution agitation via bath recirculation, stirrers, ultrasonic devices and/or megasonic devices is typically employed. Nonetheless, boundary layer effects associated with variations in the level of solution agitation need to be taken into account, especially those resulting from equipment malfunctions.

Instrumental methods for monitoring wet processes based on electrochemical and spectroscopic analyses have been reported in the following patents, which are considered to be representative of the state of the art.

U.S. Pat. No. 5,097,130 to Koashi et al. describes a method based on near-infrared (NIR) spectroscopy for quantitative analysis of solutions, such as etchants and cleaning solutions, used to etch silicon oxide layers during semiconductor processing. In this case, solution absorbance at a specific wavelength in the NIR range from 800 to 1400 nm was predetermined to reflect the concentration of a specific species to be controlled. As discussed in paragraphs [0006]-[0010] above, however, numerous species that are effective etchants, including etchant dissociation products and byproducts of the etching reactions, are typically present in the etchant solution and take part in complex equilibria as well as the etching process. Consequently, only limited control over the etching process can be exercised by analyzing and controlling selected individual etchant species, as taught by the '130 patent.

U.S. Pat. No. 6,203,659 to Shen et al. describes a method and apparatus for monitoring degradation of a photoresist stripper bath by detecting buildup of photoresist species via light absorption by the bath. This approach is not suitable for solutions comprising a plurality of reactive species.

U.S. Pat. No. 6,270,986 to Wong describes a method of preparing and preserving biological tissue specimens for infrared spectroscopic analysis that avoids the effects of polymorphs. Sample preparation in this case involves solvent evaporation to form a dried film on an optically transparent window. This approach is not amenable to on-line analysis.

U.S. Pat. No. 5,893,046 to Wu et al. describes a method for real-time monitoring of reacting chemicals in a semiconductor manufacturing solution via electromagnetic radiation absorption measurements. This method requires that the absorbance measured for each solution constituent be compared with that measured for a standard, which is not feasible for real-time analysis of a system comprising a plurality of reactant species. In addition, the apparatus disclosed by Wu '046 utilizes a bandpass filter for wavelength selection, which typically does not provide the spectral resolution needed to identify each of several bath constituents simultaneously. For more complex processes involving numerous active reactants and byproducts and complex equilibria, measurements of the individual reactant concentrations is not a viable approach for controlling the process. The resolution provided by bandpass filters is inadequate for development of the complex algorithms required for control of such complex processes.

In view of the limitations of the prior art for analysis and control of processing solutions, there is a need for an apparatus providing real-time analysis of chemical processing solutions comprising a plurality of reactant species.

SUMMARY OF THE INVENTION

The present invention provides an apparatus based on spectroscopic analysis and chemometric data manipulation for real-time analysis and control of a process comprising a chemical reaction involving a chemical reactant and a solid in a processing solution. Generally, the apparatus measures absorption spectra for the processing solution, preferably for wavelengths in the near infrared (NIR) range from 700 to 2500 nm, and analyzes such spectral data via statistical analysis and chemometric manipulation to provide a measure of the reaction rate of the chemical reaction. The apparatus may also measure concentrations and changes in concentration of chemical reactants and reaction byproducts in the processing solution.

The data analysis typically involves differentiating spectra and extracting optical densities and wavelength shifts for the various spectral features. A model for predicting the reaction rate of the chemical reaction based on the combined effects of individual chemical reactants in the processing solution is developed by correlating spectral data measured for the processing solution with corresponding reaction rates measured by a conventional method. Measured spectral data and reaction rates are typically fitted to the model via a regression analysis method, principal component analysis, partial least squares analysis, multiple linear regression analysis, or neural network analysis, for example.

The apparatus of the invention comprises: (1) an electromagnetic radiation source operative to provide a measurement beam, and preferably a reference beam, of electromagnetic radiation; (2) a sampling element containing a test solution, which may be either a calibration solution or a sample of the processing solution; (3) an optical element operative to pass the measurement beam through the test solution; (4) a first fiber optic transmission element operative to transmit the measurement beam from said electromagnetic radiation source to said optical element; (5) a detector operative to measure the intensity of the measurement beam passed through the test solution as a function of the electromagnetic radiation wavelength over a predetermined spectral region so as to generate a spectrum of the test solution; (6) a second fiber optic transmission element operative to transmit the measurement beam passed through the test solution from said optical element to said detector; and (7) a processor including an algorithm operative to determine the rate of the chemical reaction for the processing solution by comparing spectral data for the processing solution with a model and database developed by chemometric manipulation of spectral data for calibration solutions.

The apparatus of the invention is especially useful for providing real-time ex situ dynamic chemical analysis and control of etchant solutions, 1:5 or 1:50 hydrofluoric acid (HF), for example, used for processing semiconductor wafers comprising silicon, silicon oxide and silicon nitride, for example. In a preferred embodiment, the apparatus comprises a high-resolution near-infrared (NIR) spectrometer that provides high-resolution spectra over the NIR wavelength range from 700 to 2500 nm in a sufficiently short time for on-line use. In another preferred embodiment, the apparatus monitors the etch rate provided by the etchant solution and automatically makes chemical additions and process changes to maintain the etch rate at a predetermined value.

In a preferred embodiment, the apparatus of the invention functions as an etch rate meter, acquiring and analyzing NIR spectral data for the etchant solution so as to directly determine the etch rate, without determining the concentrations of the individual etchant species in the etchant solution. The etch rate meter measures the etch rate accurately in freshly prepared baths, aged baths, and in baths with a plurality of etchant species, whether bath circulation is operative or inoperative. The etch rate meter may be used in conjunction with manual chemical additions or an automated chemical delivery system (CDS). After calibration, the etch rate meter obviates the need for periodic wafer testing to determine the etch rate, providing considerable savings in time and expense.

In further preferred embodiments, the etch rate meter may be configured to provide an alert, an alarm and/or an appropriate corrective action when a deviation in a process condition outside preset limits is detected. Process deviations that may be detected include high or low etch rate, insufficient or excessive etchant concentration, etch rate fluctuations due to an unstable chemical, presence of an extraneous chemical (added in error), and a circulating pump malfunction. The etch rate meter may also be configured to detect a bubble in the solution in the sampling element. In another preferred embodiment, the etch rate meter further provides the concentration of each of a plurality of etchant species in an etching solution.

Although the invention is described primarily with respect to control of semiconductor etching processes, the apparatus of the invention may also be applied to various other processes involving a chemical reactant and a solid in a processing solution. For example, cleaning solutions, especially those used by the semiconductor industry, often contain mild etchants, in addition to wetting agents and detergents, so that the apparatus of the invention is directly applicable to analysis and control of such systems. Within the scope of the invention, the apparatus, as described, may be applied to analysis and control of any processing solution involving a chemical reaction, a chemical reactant and a solid.

The present invention will be more fully understood from the following detailed description of the preferred embodiments thereof, taken together with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an apparatus for analysis of a sample of a processing solution employing a near infrared (NIR) measurement system in accordance with a preferred embodiment of the present invention.

FIG. 2 depicts a sampling element comprising a sample tube and an optical element comprising a pair of probes and a holder for use with the apparatus of FIG. 1.

FIG. 3 illustrates an etch rate meter according to the invention installed to provide closed-loop process control of a typical wet station used for semiconductor wafer etching.

FIG. 4 is a simplified flowchart for developing an algorithm for real-time control of an etching process using the apparatus of the invention.

FIG. 5 illustrates application of the near infrared (NIR) apparatus of FIG. 1 to control multiple baths of a wet station.

FIG. 6 shows a series of NIR spectra recorded on-line for an etchant solution comprising 50:1 hydrofluoric acid.

FIG. 7 shows a second derivative of a spectrum of FIG. 6 in accordance with a preferred embodiment of the present invention.

FIG. 8 shows a correlation curve of the etch rate of silicon dioxide in an HF 50:1 bath measured by the etch rate meter of the invention versus the etch rate determined by laboratory thickness measurements.

FIG. 9 shows second-derivative NIR spectra for an HF 50:1 etchant solution (FIG. 6) and an HF 5:1 etchant solution.

FIG. 10 shows a correlation plot of the hydrogen peroxide concentration measured by the NIR apparatus of the invention versus that measured by a standard laboratory procedure for an SC1 cleaning bath.

FIG. 11 is a graph showing the effect of a water addition on the etch rate measured by the etch rate meter of the invention for an HF 50:1 etching bath as a function of time.

FIG. 12 is a graph showing the effect of a hydrofluoric acid addition on the etch rate measured by the etch rate meter of the invention for an HF 50:1 etching bath as a function of time.

FIG. 13 is a graph illustrating the effect of temperature on the etch rate measured by the etch rate meter of the invention for an etchant solution as a function of time.

FIG. 14 is a graph illustrating the effect of stopping a circulating pump for an HF 50:1 etching bath on the etch rate measured as a function of time by the etch rate meter of the invention.

FIG. 15 is a graph illustrating the effect of gas bubbles in the sampling tube on the etch rate measured as a function of time by the etch rate meter of the invention.

FIG. 16 is a plot of etch rate values measured on-line by the etch rate meter of the invention for an HF 50:1 production etching bath as a function of time over nine days.

FIG. 17 shows plots of the concentrations of hydrogen peroxide and ammonium hydroxide measured for an SC1 cleaning bath as a function of time using the apparatus of the invention.

FIG. 18 shows plots of the concentrations of hydrogen peroxide and hydrogen chloride measured for an SC2 cleaning bath as a function of time using the apparatus of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Terminology used in this document is generally known to those skilled in the art. Unless indicated otherwise, the terms “etching solution”, “etching bath” and “bath” generally refer to solutions having the same composition but the word “bath” denotes the solution in a tank or reservoir in a production process. Likewise, a “processing solution” and a “processing bath” have the same composition but the processing bath is contained in a tank or reservoir in a production process. The adjective “fiber optic” denotes an optical transmission element comprising at least one optical fiber. A “fiber optic probe” generally comprises a plurality of bundled optical fibers. Absorption (and transmission) spectra were conventionally recorded by scanning the wavelength of electromagnetic radiation incident on the sample but modern spectrometers typically employ a detector array that detects all wavelengths comprising a spectrum simultaneously or in a short time. The term “scanning” encompasses spectra generated using a detector array.

The apparatus of the invention provides real-time dynamic analysis and control of a process comprising a chemical reaction involving a chemical reactant and a solid in a processing solution. The solid may be an insulator, a semiconductor or a metal. For semiconductor etching processes, the solid typically comprises silicon, silicon oxide or silicon nitride, or combinations thereof. The analysis comprises determining the reaction rate of the chemical reaction and may further include determining the concentration of at least one chemical reactant in the processing solution, the change in concentration of at least one chemical reactant in the processing solution, and the rate of disappearance or appearance of at least one chemical reactant in the processing solution. The apparatus may include a chemical correction system for making additions of at least one chemical reactant and/or water to the processing solution (based on the analysis data) to maintain the rate of the chemical reaction within preset limits.

The apparatus of the invention is especially useful for providing real-time ex situ dynamic chemical analysis and control of etchant solutions used for processing semiconductor wafers comprising silicon, silicon oxide and/or silicon nitride. The apparatus of the invention may be used to analyze a wide range of etchant solutions containing a wide range of etchant species and counterions. These include aqueous solutions comprising at least one chemical species selected from the group consisting of H⁺, HF, F⁻, HF²⁻, SiF₄, H₂SiF₆, SiF₆ ²⁻, OH⁻, H₂O₂, HO²⁻, S₂O₈ ²⁻, SO₄ ²⁻, SO₃ ²⁻, C₂H₃OH₂ (acetic acid), C₂H₃OH⁻, C₂H₃O²⁻, Cl⁻, Br⁻, I⁻, NH₄ ⁻, NO₃ ⁻, NO₂ ⁻ and N³⁻, and combinations thereof. The aqueous etchant solution may comprise an organic species, acetic acid, for example, or an organic solvent, ethylene glycol, for example. The invention may be used to analyze acid etchants, base (alkaline) etchants, commercial oxide etchants, commercial silicon etchants, and commercial metallic etchants, for example. Common etchants that may be analyzed include HF:H₂O, HF1:5, HF1:50, H₂S0₄:HNO₃:HF, acetic acid:NH₄F, H₃PO₄:HNO₃:acetic acid, HNO₃:HF, H₂SO₄:H₂O₂, H₂SO₄:HNO₃, H₂SO₄:persulfate, ethylene glycol+HF, and buffered oxide etch (BOE). An etchant species may be dissolved or suspended in the etchant solution, and may be added as a solid or liquid, or be conveyed in a gaseous phase.

The apparatus of the invention may also be used to provide real-time dynamic analysis and control of other semiconductor processing solutions, including surface preparation and cleaning solutions. Typical constituents of such solutions include H₂O₂, O₃, NH₄OH, HCl, HF H₂SO₄, HNO₃, acetic acid, and combinations thereof. Common semiconductor cleaning solutions include SC1 (H₂O₂+NH₄OH) and SC2 (H₂O₂+HCl).

The apparatus of the invention is based on near infrared (NIR) spectroscopic analysis in the 700 to 2500 nm wavelength range, which can be used to detect both inorganic and organic species in solution. Absorption by chemical species in this wavelength range involves chemical bond vibrations, overtones, and combinations thereof. In addition to providing quantitative analysis of an analyte in a specific matrix (solution environment), NIR spectroscopy is also sensitive to physical characteristics of the matrix, including density, viscosity and texture.

The apparatus of the invention for determining the rate of a chemical reaction involving one or more chemical reactants and a solid in a processing solution, comprises: (1) an electromagnetic radiation source operative to provide a measurement beam, and preferably a reference beam, of electromagnetic radiation; (2) a sampling element containing a test solution, which may be either a calibration solution or a sample of the processing solution; (3) an optical element operative to pass the measurement beam through the test solution; (4) a first fiber optic transmission element operative to transmit the measurement beam from said electromagnetic radiation source to said optical element; (5) a detector operative to measure the intensity of the measurement beam passed through the test solution as a function of the electromagnetic radiation wavelength over a predetermined spectral region so as to generate a spectrum of the test solution; (6) a second fiber optic transmission element operative to transmit the measurement beam passed through the test solution from said optical element to said detector; and (7) a processor including an algorithm operative to determine the rate of the chemical reaction for the processing solution. The electromagnetic radiation source is preferably a halogen lamp, which provides electromagnetic radiation in the near infrared (NIR) spectral region from 700 to 2500 nm, but any other suitable electromagnetic radiation source may be used.

In order to measure the rate of the chemical reaction, the measurement beam is passed through the test solution at at least two points in time and spectra of the test solution are generated at the two or more points in time. For one of the minimum two points in time, the test solution is a calibration solution for which the rate of the chemical reaction is measured by a standard procedure. For the other of the minimum two points in time, the test solution is a sample of the processing solution. The spectrum generated for the sample is compared to the spectrum generated for the calibration solution to determine the rate of the chemical reaction in the processing solution.

Preferably, spectra are generated for a plurality of calibration solutions to provide a calibration database that can be used for accurate determination of the rate of the chemical reaction. The plurality of calibration solutions preferably comprise samples of the same production processing bath for which spectra are generated according to the invention and rates of the chemical reaction are measured by a standard procedure at different times to provide a training set of data. The concentrations of reactants, reaction byproducts and other constituents of the calibration solutions need not be known. It is preferable that at least one of the constituents be present at substantially different concentrations in at least two of the calibration solutions. Appreciable variations in the concentrations of reactants and reaction byproducts generally occur naturally during use of the production processing bath. Wider variations in the concentrations of the bath constituents needed to provide an adequate database for determining the rate of the chemical reaction for a bath sample may be provided by adding bath constituents to the production processing bath or to separate calibration solutions. After an adequate database and a model have been developed, a spectrum generated for a sample of the processing bath can be used to provide the rate of the chemical reaction for the processing bath.

In a preferred embodiment, the sampling element comprises a tube of a substantially NIR-transparent material and a liquid pump for flowing the test solution from the processing bath through the tube. Preferably, the test solution is circulated from the bath, through the tube, and back to the bath, continuously or intermittently. The analysis of the invention may be performed on a stagnant bath sample or on a flowing stream of the processing solution. The sampling element may have any suitable geometry, and may include a separate sample chamber.

In a preferred embodiment, the sampling element comprises a substantially NIR-transparent tube and the optical element comprises a mechanical clamp with a circular hole that fits snugly around the sampling element tube and secures and positions (via small holes perpendicular to the tube) fiber optic transmission elements so as to convey the measurement beam transversely through the tube. Preferably, attachment of the optical element and the fiber optic transmission elements does not substantially depress or distort the sampling element tube, or other sample container. Suitable NIR-transparent materials include, but are not limited to, Teflon, glass, polyethylene, polypropylene, PET, polyvinylchloride, Nylon, Tygon, polystyrene, silicone rubber PVA, and quartz.

The preferred optical element of the invention, which attaches to a sampling element tube, may be installed in a semiconductor wet bench or wet station. Wet etching of semiconductor wafers typically involves immersion of one or more wafers in an etching bath (contained in a tank) for a predetermined period of time, or spraying the etching solution onto the wafer surface for a predetermined period of time. In both cases, the liquid etching solution is circulated to achieve better contact between the liquid and the wafer surface, and to remove etching by-products and particles adhering to wafer surface. After being etched, the wafer is rinsed and dried, and may be cleaned in a cleaning solution, H₂O₂+NH₄OH (SC1), H₂O₂+HCl (SC2) or H₂O₂+H₂SO₄, for example. An “automated wet station” performs the entire wet etching process under computer control and robotic transfer of the wafers, and controls and monitors key parameters such as temperature, bath circulation and etch time. The apparatus of the invention is ideally suited for use in an automated wet station.

The detector of the apparatus of the invention is operative to measure the intensity of the measurement beam passed through the test solution as a function of the electromagnetic radiation wavelength over a predetermined spectral region. Although the predetermined spectral region may comprise only a portion of the NIR spectral range from 700 to 2500 nm, the predetermined spectral region preferably comprises all of the NIR range so as to provide as much information as possible.

The spectral data provided by the detector typically comprise the optical density (absorbance) of the test solution as a function of wavelength of the electromagnetic radiation. The optical density may be expressed as absorbance or transmission of the test solution using any suitable units. Optical density values are preferably corrected for variations in the intensity of the electromagnetic radiation source based on the intensity of a reference beam, as is well known in the art. This corrective function may be performed by the processor of the invention, or by a second processor in a commercial spectrometer incorporated in the apparatus of the invention. The term “processor” encompasses such a second processor.

Spectral data indicative of the optical properties of a test solution include the magnitude, wavelength and bandwidth (broadness) of peaks and shoulders in spectral plots (spectra) of radiation absorbance or transmission as a function of wavelength, as well as plateaux, especially those corresponding to the absence of absorbing species. A peak (or shoulder) in an absorption spectrum typically corresponds to radiation absorption by a specific constituent of the test solution but the peak height, bandwidth and wavelength are affected by other solution species comprising the environment of the constituent. A change in the optical properties of the processing solution may be indicated by a change in the magnitude, wavelength or bandwidth of a peak, appearance or disappearance of a peak or shoulder, or a subtle wavelength shift for a spectral feature, for example. In a preferred embodiment of the invention, spectral features are accented by taking the first or second derivative of the spectrum. The first derivative, for example, converts an indistinct inflection point into a peak, which is more easily quantified.

The algorithm incorporated in the processor of the apparatus of the present invention extracts information from NIR spectral data (optical density as a function of wavelength) using various mathematical and statistical data analysis methods, which taken together comprise chemometrics. The data analysis methods are selected to enhance spectral features so as to emphasize the effects of analyte concentration and matrix properties. A typical first step is to take a derivative (first or second) of the spectra to accent spectral features. The derivative spectra is then regressed and used to predict chemical and physical properties of the analyte and solution matrix that produce spectral effects such as wavelength band height changes and band shifting. Appropriate regression techniques include principal component analysis, partial least squares analysis, multiple linear regression and neural network analysis.

A model is developed and incorporated in the algorithm in the processor for predicting reaction rate of the chemical reaction based on the combined effects of individual chemical species in the processing solution. The model is developed by correlating spectral data measured for the processing solution as a function of time with corresponding reaction rates measured by a conventional method. Measured spectral data and chemical reaction rates are typically fitted to the model via the selected regression analysis method or methods.

The chemometrics method may also be used to compare a given spectra with a defined fingerprint of a specific sample set. This allows a given spectra to be identified as a specific entity separate from the others. In this case, collected spectra are compared with the database set, providing detection of even slight changes in the sample solution. The sample may then be rejected or tested further to determine the cause of the spectral change.

Procedures that may be used to refine the algorithm incorporated in the processor of the invention include spectral identification and spectra qualification. Spectral identification is designed to provide positive identification of a given constituent in a solution and to eliminate the possibility that the constituent will be falsely identified as another chemical. This is accomplished by combining available databases into a new database, and performing a chemometric manipulation using various data pretreatments separately and in combination. Suitable data pretreatments include spectral correlation, maximum spectral distance, Mahalanobis distance, and residual in principal component space, and combinations thereof. Spectra qualification involves the same methodology as spectral identification but is applied to a given bath constituent. Qualification parameters are typically tighter and the resulting model can identify slight changes in a new spectrum.

The processor with the included algorithm is operative to analyze the spectral data and perform a chemometric data manipulation so as to determine the reaction rate of the chemical reaction. In preferred embodiments, the processor may further: (a) convert an optical property of a chemical reactant into a concentration of the chemical reactant in the processing solution; (b) convert a change in an optical property of a chemical reactant into a change in the concentration of the chemical reactant in the processing solution; (c) convert a differentiated change in an optical property of a chemical reactant in the processing solution into a rate of change of the concentration of the chemical reactant in the processing solution; (d) convert an optical property of each of a plurality of chemical reactants in the processing solution into a concentration of each of the plurality of chemical reactants in the processing solution; (e) convert a change in an optical property of each of a plurality of chemical reactants in the processing solution into a change in the concentration of each of the plurality of chemical reactants in the processing solution; and (f) convert a differentiated change in an optical property of each of a plurality of chemical reactants in the processing solution into a rate of change of the concentration of each of the plurality of chemical reactants in the processing solution.

The processor of the apparatus of the invention and the algorithm therein are operative to determine the rate of a chemical reaction involving one or more chemical reactants and a solid in a processing solution by effecting the steps of an analysis method, comprising: (1) generating spectra over the predetermined spectral region for a plurality of calibration solutions each comprising at least some of the constituents of the processing solution, wherein the constituents include the chemical reactants and byproducts of the chemical reaction, and at least one of the constituents is present at different concentrations in at least two of the calibration solutions; (2) measuring the rate of the chemical reaction for the plurality of calibration solutions using a standard procedure; (3) correlating the spectra generated for the plurality of calibration solutions and the chemical reaction rates measured by the standard procedure for the plurality of calibration solutions via a chemometric data manipulation to develop a calibration model and a calibration database; (4) generating a spectrum over the predetermined spectral region for a sample of the processing solution; and (5) comparing the spectrum generated for the sample of the processing solution with the calibration database to determine the rate of the chemical reaction for the processing solution. The concentrations of reactants, reaction byproducts and other constituents of the calibration solutions need not be known.

Preferably, the calibration solutions used to develop the calibration model comprise samples of a production processing bath. Development of the calibration model should involve relatively wide variations in the important variables, including concentrations of constituents of the processing solution, solution flow rates and bath temperature, for example. It is usually necessary to add at least some of the processing solution constituents to production processing baths to provide sufficiently wide concentration variations for model development.

DESCRIPTION OF A PREFERRED EMBODIMENT

In a preferred embodiment, the apparatus of the invention comprises a commercial NIR spectrometer that includes an electromagnetic radiation source and a suitable scanning detector in the same unit, and preferably provides a reference beam. The NIR spectrometer should provide high spectral resolution, low instrumental noise, and high signal-to-noise ratio so that even small optical density changes and subtle spectral shifts associated with millimolar processing solution concentration changes can be detected. Commercial spectrometers typically provide a full NIR scan in less than one minute, which is sufficiently fast for close control of etching processes.

Any suitable spectrometer may be used to practice the invention. A suitable commercial NIR spectrometer is the Near Infrared Scanning Process Multiplexing Spectrometer 25, which comprises a halogen lamp, a grating monochromator and an InGaAs detector. Alternatively, a dual detector system may be employed, comprising a silicon detector for the 700-1100 nm wavelength range and a PbS detector for the 1100-2500 nm range. This instrument operates over the NIR wavelength range from 700 to 2500 nm, and provides a full scan in less than one second. The instrumental noise is less then 0.0003 absorbance units (AU) rms over a 3-AU range. The wavelength accuracy (SD) based on an accepted wavelength standard is less then 0.30 nm. The spectral bandwidth is less than 10 nm±1 nm. This instrument may operate in the transmission or reflection mode. Any NIR spectrometer with substantially comparable specifications may be used in the apparatus of the invention.

FIG. 1 depicts an apparatus 20 for analysis of a sample of a processing solution using a near infrared (NIR) spectrometer in accordance with a preferred embodiment of the present invention. Apparatus 20 comprises a spectrometer system 25, which includes an electromagnetic radiation source 32, and a main channel 36 for transfer of a measurement beam via a first fiber optic probe 40 to an optical element 45 containing the sample solution. Optical element 45 is described in further detail with respect to FIG. 2. A second fiber optic probe 44 transfers the measurement beam passed through the sample from optical element 45 to a detector 62 (via optical multipexer 46, mirror 50, lens 54 and grating 56). Optical multiplexer 46 is operative to receive electromagnetic radiation from a multiplicity of fiber optic probes, such as fiber optic probe 44. Electromagnetic radiation source 32 also provides a reference beam to detector 62 (via mirror 50, lens 54 and grating 56).

Detector 62 is operative to receive the incoming electromagnetic radiation from an order sorter and to receive wavelength standards from a wavelength standards element 68. The detector provides an output of optical density data of the sample solution over a spectral range, such as the near infrared range (700 to 2500 nm).

A processor 64 on a control board receives the optical density data of the processing solution from detector 62, as well as the intensity of the reference beam. Generally, processor 64 provides an optical density value of the test solution corrected for variations in the intensity of radiation source 32 via the reference beam. The processor also performs a chemometric manipulation of data received from detector 62.

FIG. 2 shows a more detailed view of optical element 45 and fiber optic probes 40 and 44 of FIG. 1, and also depicts a sampling element comprising a sampling element tube 43 (through which a test solution comprising a calibration solution or a sample of a processing solution is circulated). Optical element 45 fits snugly around sampling element tube 43 and holds fiber optic probes 40 and 44 perpendicular to the axis of sampling element tube 43, which comprises a material that is transparent to NIR radiation (Teflon, for example). A measurement beam 41 is transmitted via fiber optic probe 40 to optical element 45, passes through sampling element tube 43 and the test solution therein, and is transmitted from optical element 45 via fiber optic probe 44 to detector 62 (FIG. 1). Fiber optic probes 40 and 44 are typically about 2.5 cm in diameter and comprise a bundle of anhydrous quartz optical fibers (1 mm in diameter and 6 m long) encased in a stainless steel sheath with a sapphire window 42 at the end.

The optical probe/sampling tube device depicted in FIG. 2 offers significant advantages. Optical element 45 holds sampling element tube 43 and fiber optic probes 40 and 44 rigidly in a fixed geometry without depressing the tube so as to maintain the constant probe spacing and path length needed for accurate and reproducible results. Optical element 45 also provides shielding against stray light. In addition, the probes do not contact the sample solution and are protected from the production environment (a wet station, for example). The sampling element tube may also be part of the tubing system normally used to circulate and filter the processing solution (etching solution in a wet station, for example) so that a special sampling system is not required. In this case, installation of the apparatus of the invention in production typically requires only that two one-inch holes be drilled to accommodate the fiber optic probes.

FIG. 3 illustrates an etch rate meter 20 according to the invention installed to provide closed-loop process control of a typical wet station 100 used for semiconductor wafer etching. Wet station 100 comprises etching baths 110 and 114, rinse baths 112 and 116, cleaning baths 118 (SC1) and 122 (SC2), rinse baths 120 and 124, and a drying stage 126. The etching process involves the sequence etch-rinse-clean-rinse-dry, wherein wafers are sequentially immersed in each type of bath for a predetermined time via a robotic system under computer control. Etch rate meter 20 preferably analyzes etching baths 110 and 114, and optionally one or more of the other baths, and inputs the analysis data to a computer 130. The analysis data are passed from computer 130 to a standard digital/analog I/O controller 140, which dynamically integrates etch rate meter 20 into the wet station control system via a closed loop to ensure that the correct etching bath chemicals are present, and that their concentrations and the etch rate are within preset control limits. This is accomplished via an automated wet station (AWS) controller 150, which signals a chemical delivery system (CDS) 170 to adjust the etch rate of etching bath 110 and/or 114 by adding appropriate chemicals via a valve 160. Controller 150 may also sound an “out of specification” alarm when appropriate. A separate AWS controller 190 may be used to add another chemical or water to etching bath 110 and/or 114. Etch rate meter 20 is controlled by chemometric software having calibration, identification and routine operation capabilities. Custom software based on the SECS protocol was developed for interfacing the process spectrometer operational software, data collection system, and the AWS controller.

Two regression techniques, principal component analysis (PCA) and partial least squares (PLS) analysis, were used to develop an algorithm for the preferred embodiment of the invention described below. The procedure used to develop the algorithm is described in ASTM E1790-00 entitled “Standard Practice for Near Infrared Analysis”, which is hereby incorporated by reference. The PCA method resolves sets of data, such as NIR spectra, into orthogonal components whose linear combinations approximate the original data to any desired degree of accuracy. This regression method divides the spectral data into the most common variations (factors, eigenvectors, loadings) and the corresponding scaling coefficients (scores). The PLS analysis relates several response variables to several explanatory variables, and deals efficiently with data sets comprising numerous variables that are highly correlated and involve substantial random noise.

The methodology for development of a chemometric-based algorithm according to a preferred embodiment of the invention may be divided into three stages. In the training stage, a data set is generated via NIR spectral measurements. In the application stage, standard commercialized software is applied to the data set generated in the training stage. A preferred software package is Vision™ produced by Foss-NIRSystem Inc. (Maryland, USA) but any suitable software package may be used. In the production stage, an algorithm based on a model is produced via a regression analysis and chemometric data manipulation, which can be applied to analyze unknown samples so as to determine at least one of a reaction rate and a concentration of a chemical reactant in a processing solution. The reaction rate is generally determined without reference to the concentrations of reactants, reaction byproducts or other constituents of the processing solution.

An algorithm model for predicting etch rate and measuring the concentrations of etching bath constituents was developed by first measuring NIR spectra for fresh and aged etching baths (calibration solutions) for which the concentrations of bath constituents were varied over wide ranges. Aged baths were production baths used to etch wafers and contained byproducts of the etching process. The effects of various bath recirculation rates (including stagnant baths) and temperature were also determined. Etch rates for use in calibrating the algorithm model were determined by the standard method of measuring the wafer silicon oxide layer thickness before and after the wafer was immersed in the etching bath for a given time period (and then rinsed and dried). Test wafers used to determine the etch rate based on thickness measurements were 6-inch silicon wafers with a homogenous 6000-angstrom silicon oxide layer. Thickness of the silicon oxide layer was measured with a FT layer thickness-measuring tool (several measurements were averaged).

All algorithm development involved a wet processing production line tool located in a wafer production site. The Automated Wet Station (AWS) was a commercial type comprising an HF etching bath, SC1 and SC2 cleaning baths, a quick-rinse-and-dump deionized water bath, and a wafer spin-rinse dryer. Wafers were handled robotically under computer control. All chemicals and water used were microelectronics grade. Spectra for use in model development were measured during the wafer etching process and could be directly related to the process conditions and the etch rate determined by thickness measurements.

The algorithm model was developed for an HF 50:1 bath containing 1% HF in deionized water. The etch rate was increased by adding 10% HF solution to the bath, and was decreased by adding deionized water. After each addition, the bath was recirculated for sufficient time for thorough mixing before wafers were tested. The etch rate was varied by 20% above and below the target value (5% above and below the control limits). Baths were aged up to two weeks and were used to process different types of wafers. The actual concentrations of etchant species in the bath were determined by analyzing a sample taken at the time of the NIR measurement by conventional analytical methods.

FIG. 4 is a simplified flowchart for developing an algorithm for real-time control of an etching process using the apparatus of the invention. In an acquisition step 310, a large number of calibration samples of the etching bath are analyzed by NIR spectroscopy (using the apparatus of invention) and by conventional analytical methods, and the results are included in a database. In an identifying step 320, a new spectrum is compared with spectra in the database and a spectral feature is identified with a specific chemical constituent in the bath. The identification is effected by using computer 130 (FIG. 3) to compare the measured spectrum with standard spectra for the bath constituents, as well as the boundary limits and set points for each constituent in each of the baths in the wet station. In a decision stage 330, computer 130 checks whether the spectral identification is within the acceptable set of one or more constituents of the bath.

If the spectrum is positively identified, computer 130 (FIG. 3) or processor 64 (FIG. 1) accepts the spectrum as having been positively identified. The acceptance indication is passed on to a calculation stage 340, in which the computer or processor performs calculations of concentrations and etch rates of the wafers as a function of the spectral data received from spectrophotometer 25.

If the spectrum is not positively identified in stage 330, computer 130 passes the information to a negative indication stage 360. Typically at stage 360, the computer identifies whether the spectrum can be attributed to another known chemical, a bubble, or a pump failure. If the chemical is not known, the computer passes this information to the AWS controller 150 (FIG. 3). If another indication of a bubble or pump failure is detected, the computer passes this information to a system circulation analysis step 380. In step 380, it is discerned whether the fault is a bubble or a pump failure, based on a spectrum identification algorithm. Step 380 outputs a result that defines whether the fault was a bubble or pump failure. In the case of a bubble, step 380 relays an instruction to repeat acquisition step 310. In the case of a pump failure, step 380 inputs this information to AWS controller 150 (FIG. 3A), which typically activates an alert.

In a concentration acceptance stage 350 (FIG. 4), the computer checks if the bath constituent concentration and/or etch rate received from stage 330 falls within acceptable control/statistical limits. If the concentration and/or etch rate is in the acceptable range, then system 20 (FIG. 1) is ready to acquire another spectrum, or to proceed to measure parameters of another bath. Data may be sent to the data collection system and the processed wafer history may be updated by computer 130, with the data collected when the wafer was processed in a bath.

If the bath etch rate and/or constituent concentration is not within the accepted range, then the computer passes a signal to AWS controller 150. If a wrong chemical has been added or other serious error has occurred, stage 330 sends a failure message and an alert to the AWS controller 150 and the bath is taken out of service until corrective action has been taken.

In order to develop a model for determining etch rates and/or chemical concentrations based on NIR spectral data, various chemometric methods and manipulations were applied to the data. These methods included data pretreatments such as detrend, multiplicative pretreatment, and taking the n^(th) derivative of the spectra. The resulting database was PLS analyzed to establish a modeling relationship between the spectra and the bath constituent. Varying the analysis parameters, such as the data pre-treatment, produced various models. Approximately 15% of the spectra in the database were set aside for validation of the various models. For each model tested, the standard error of the model, the standard error of the validation sets, and the R2 values were recorded. Promising models were tested for real-time predictive capability to identify the best model for a given bath constituent.

FIG. 5 illustrates application of the near infrared (NIR) apparatus of FIG. 1 to control multiple baths of a wet station. Optical probes 44 from wet station baths are connected to multiplexer 46 (FIG. 1). Apparatus 20 analyzes the optical inputs from multiplexer 46, and provides data to computer 130. Wet station controller 150 receives inputs from computer 130, and activates wet station controller 150.

FIG. 6 shows a series of NIR spectra recorded on-line for an HF 50:1 bath. These spectra correspond to slightly different HF concentrations resulting in differences in the measured etch rates. Shifts in the peak intensities and baseline are evident.

FIG. 7 shows a second derivative of a spectrum of FIG. 6 in accordance with a preferred embodiment of the present invention. Such second derivative spectra were used for chemometric modeling based on 140 calibration samples of the HF 50:1 bath.

FIG. 8 shows a correlation curve of the etch rate of silicon dioxide in an HF 50:1 bath measured for 140 calibration samples by the etch rate meter of the invention, versus the etch rate determined by laboratory thickness measurements. A good correlation (R>0.97) is evident. Similar results were obtained for an HF 5:1 bath, as indicated by the data in Table 1 (ER=etch rate range in Angstroms/second; No.=number of samples).

TABLE 1 Validation Test Results for HF 50:1 and HF 5:1Etching Baths Calibration Validation Bath ER No. R Std. Error No. R Std. Error 50:1 0.8-1.35 140 >0.96 0.04 32 0.93 0.05  5:1   8-12.5 130 >0.97 0.25 28 0.95 0.35

FIG. 9 shows second-derivative NIR spectra of an HF 50:1 etchant solution (FIG. 7) and an HF 5:1 etchant solution. The difference in the HF concentration is seen to produce different spectral “fingerprint” patterns. Such fingerprints were especially useful for identifying bath constituents so as to avoid production processing with the incorrect chemicals, which is a significant problem often resulting in hundreds of scrap wafers.

Methodology similar to that used for HF etching baths was used to develop models for SC1 (H₂O₂+NH₄OH) and SC2 (H₂O₂+HCl) semiconductor cleaning baths. Bath spectra were recorded on-line by the etch rate meter of the invention, and chemical concentrations were determined off line using classical analytical methods. The results were regressed against each other to create the concentration algorithms. Samples in the training sets for SC1 and SC2 chemometric modeling comprised samples from baths in a production line. The sets included samples from fresh baths, diluted baths, baths with different solution recirculation rates, and aged baths used up to 24 hours to process different types of wafers. As was the case for the HF baths, training sets for the SC1 and SC2 baths represented real bath conditions so as to provide an accurate, precise and robust calibration model. This is particularly important for baths having unstable or volatile reactants (H₂O₂, NH₄OH and O₃, for example) that are rapidly depleted.

FIG. 10 shows a correlation plot of the hydrogen peroxide concentration measured by the NIR apparatus of the invention versus that measured by a standard laboratory procedure for an SC1 cleaning bath. An excellent correlation (R>0.98) was observed. Relative standard errors of less then 5% were calculated for hydrogen peroxide determinations by NIR measurements for both the SC1 and the SC2 bath.

FIG. 11 is a graph showing the effect of a water addition on the etch rate measured by the etch rate meter of the invention for an HF 50:1 etching bath. Dilution of the bath with water reduces the etch rate.

FIG. 12 is a graph showing the effect of a hydrofluoric acid addition on the etch rate measured by the etch rate meter of the invention for an HF 50:1 etching bath. Addition of the HF etchant to the bath increases the etch rate. As discussed with respect to FIG. 3, etch rate meter 20 automatically signals automated wet station (AWS) controller 150 to add the appropriate amount of HF when the etch rate is substantially below target, and to add the appropriate amount of water when the etch rate is too high.

FIG. 13 is a graph illustrating the effect of temperature on the etch rate measured by the etch rate meter of the invention for an HF 5:1 etching bath as a function of time. Such data may be used to correct measured etch rates for temperature variations.

FIG. 14 is a graph illustrating the effect of stopping a circulating pump for an HF 50:1 etching bath on the etch rate measured as a function of time by the etch rate meter of the invention. Circulating pump stoppage is indicated by etch rate values that are relatively constant, rather than slowly undulating with time.

FIG. 15 is a graph illustrating the effect of gas bubbles in the sampling tube on the etch rate measured for an HF 50:1 etching bath as a function of time by the etch rate meter of the invention. Gas bubbles in the sampling tube are detected as erratic changes in the measured etch rate.

FIG. 16 is a plot of etch rate (ER) values (Angstroms/second) measured on-line by the etch rate meter of the invention for an HF 50:1 production etching bath as a function of time over nine days. The etch rate is seen to change with time, reflecting expected changes in the bath composition. The overall trend is for the etch rate to steadily increase until water is added to the bath to replace that lost by evaporation and dragout so as to maintain the etch rate within the control range (8.5 to 11.5 Angstroms/second). This upward trend is due to increases in the concentrations of etchant species due to the reduction in the bath volume resulting from solvent evaporation, and to generation of more reactive etchant species, fluorosilic acids, for example, as byproducts of the HF etching process. This explanation is consistent with the bath history during the etch rate monitoring period. At mid-day on day 4, for example, HF was added to the bath, producing a step increase in etch rate (superimposed on the slowly increasing etch rate). Sharp decreases in the etch rate resulted from additions of water on days 5 and 9, and replacement of the bath acid on day 7.

The etch rate data generated by the etch rate meter of the invention (FIG. 16) was consistent with etch rates determined by thickness measurements for test wafers before and after etching. However, wafer testing, which is typically performed at 8 to 10 hour intervals or when warranted by changes in the bath operating conditions, is time consuming and requires that production be suspended for 45 to 90 minutes. The close control provided by the etch rate meter of the invention eliminates the need for wafer testing, increasing production throughput and reducing costs, and ensures that processing problems are detected and corrected quickly so that scrap rates are minimal and throughput is maximal.

Chemicals used in wafer cleaning baths tend to be unstable so that their concentrations decrease with time. In addition to measuring etch rates for etching baths, the apparatus of the invention may also be used to measure the concentrations of etchant species and cleaning bath chemicals so that they can be replenished as needed to provide optimum results.

FIG. 17 shows plots of the concentrations of hydrogen peroxide and ammonium hydroxide measured by the apparatus of the invention for an SC1 cleaning bath as a function of time. These data show that ammonium hydroxide is depleted more rapidly than hydrogen peroxide in the SC1 cleaning bath.

FIG. 18 shows plots of the concentrations of hydrogen peroxide and hydrogen chloride measured for an SC2 cleaning bath as a function of time using the apparatus of the invention. These data show that hydrogen chloride is depleted somewhat more rapidly than hydrogen peroxide in the SC2 cleaning bath.

It will be understood by those skilled in the art that aspects of the present invention may be embodied in a computer running software, and that the software may be supplied and stored in tangible media, hard disks, floppy disks or compact disks, for example, or in intangible media, such as an electronic memory or a network.

It will be appreciated by persons skilled in the art that the present invention is not limited to what has been particularly shown and described. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described, as well as variations and modifications thereof that are not in the prior art, which would occur to persons skilled in the art upon reading the foregoing description. 

1. An apparatus for determining the rate of a chemical reaction involving one or more chemical reactants and a solid in a processing solution, comprising: an electromagnetic radiation source operative to provide a measurement beam of electromagnetic radiation; a sampling element containing a test solution, which may be either a calibration solution or a sample of the processing solution; an optical element operative to pass the measurement beam through the test solution; a first fiber optic transmission element operative to transmit the measurement beam from said electromagnetic radiation source to said optical element; a detector operative to measure the intensity of the measurement beam passed through the test solution as a function of the electromagnetic radiation wavelength over a predetermined spectral region so as to generate a spectrum of the test solution; a second fiber optic transmission element operative to transmit the measurement beam passed through the test solution from said optical element to said detector; and a processor including an algorithm operative to determine the rate of the chemical reaction for the processing solution by effecting the steps of an analysis method, comprising generating spectra over the predetermined spectral region for a plurality of calibration solutions each comprising at least some of the constituents of the processing solution, wherein the constituents include the chemical reactants and byproducts of the chemical reaction, measuring the rates of the chemical reaction for the plurality of calibration solutions using a standard procedure, correlating the spectra generated for the plurality of calibration solutions and the chemical reaction rates measured by the standard procedure for the plurality of calibration solutions via a chemometric data manipulation to develop a calibration model and a calibration database, generating a spectrum over the predetermined spectral region for a sample of the processing solution, and comparing the spectrum generated for the sample of the processing solution with the calibration database to determine the rate of the chemical reaction for the processing solution.
 2. The apparatus of claim 1, wherein the electromagnetic radiation source is further operative to provide a reference beam of the electromagnetic radiation and the intensity of the measurement beam is corrected for fluctuations in the intensity of the electromagnetic radiation provided by the electromagnetic radiation source based on the intensity of the reference beam.
 3. The apparatus of claim 1, wherein the process is an etching process, the chemical reaction is a chemical etching reaction, the one or more chemical reactants comprise one or more etchant species, and the processing solution is an etching solution, such that the process comprises chemical etching of the solid by one or more etchant species in an etching solution and the reaction rate is an etch rate of the solid.
 4. The apparatus of claim 3, wherein the solid comprises a material selected from the group consisting of silicon, silicon oxide and silicon nitride, and combinations thereof.
 5. The apparatus of claim 3, wherein the etching solution comprises an aqueous solution comprising at least one chemical species selected from the group consisting of H⁺, HF, F⁻, HF²⁻, SiF₄, H₂SiF₆, SiF₆ ²⁻, OH⁻, H₂O₂, HO²⁻, S₂O₈ ²⁻, SO₄ ²⁻, SO₃ ²⁻, C₂H₃OH₂, C₂H₃OH⁻, C₂H₃O²⁻, Cl⁻, Br⁻, I⁻, NH₄ ⁻, NO₃ ⁻, NO₂ ⁻, N³⁻, and combinations thereof.
 6. The apparatus of claim 3, wherein the etching solution is selected from the group consisting of an acid, a base, HF:H₂O, HF1:5, HF1:50, H₂S0₄:HNO₃:HF, acetic acid:NH₄F, H₃PO₄:HNO₃:acetic acid, HNO₃:HF, H₂SO₄:H₂O₂, H₂SO₄:HNO₃, H₂SO₄:persulfate, ethylene glycol+HF, buffered oxide etch (BOE), a commercial oxide etchant, a commercial silicon etchant, and a commercial metallic etchant.
 7. The apparatus of claim 1, wherein the predetermined spectral region comprises at least part of the near infrared (NIR) spectral range from 700 to 2500 nm.
 8. The apparatus of claim 1, wherein said sampling element comprises a tube of a material that is substantially transparent to electromagnetic radiation in the predetermined spectral region.
 9. The apparatus of claim 8, wherein the material comprises at least one material selected from the group consisting of Teflon, glass, polyethylene, polypropylene, PET, polyvinylchloride, nylon, Tygon, polystyrene, silicone rubber PVA, and quartz.
 10. The apparatus of claim 8, wherein the processing solution is flowed through said tube.
 11. The apparatus of claim 1, wherein the steps of correlating and comparing are performed using at least one data analysis method selected from the group consisting of principal component analysis, partial least squares analysis, multiple linear regression analysis, and neural network analysis.
 12. The apparatus of claim 1, wherein a chemical reactant is present at two different known concentrations in at least two of the calibration solutions, and said processor is further operative to determine the concentration of the chemical reactant in the processing solution.
 13. The apparatus of claim 1, wherein a chemical reactant is present at two different known concentrations in at least two of the calibration solutions, and said processor is further operative to determine the rate of change in the concentration of the chemical reactant in the processing solution over a period of time.
 14. The apparatus of claim 1, wherein a chemical reactant is present at two different known concentrations in at least two of the calibration solutions, and said processor is further operative to provide a derivative function of the rate of change in the concentration of the chemical reactant in the processing solution over a period of time.
 15. The apparatus of claim 1, wherein a plurality of chemical reactants is each present at two different known concentrations in at least two of the calibration solutions, and said processor is further operative to determine the concentration of each of the plurality of the chemical reactants in the processing solution.
 16. The apparatus of claim 1, wherein a plurality of chemical reactants is each present at two different known concentrations in at least two of the calibration solutions, and said processor is further operative to determine a rate of change in the concentration of each of the plurality of the chemical reactants in the processing solution.
 17. The apparatus of claim 1, further comprising: a chemical delivery system operative to replenish at least one of the chemical reactants in the processing solution so as to increase the reaction rate of the chemical reaction, or to add water to the processing solution so as to decrease the reaction rate of the chemical reaction.
 18. An apparatus for controlling an etching process by determining the etch rate of a solid in an etching solution containing one or more etchant species, comprising: an electromagnetic radiation source operative to provide a measurement beam of electromagnetic radiation; a sampling element containing a test solution, which may be either a calibration solution or a sample of the etching solution; an optical element operative to pass the measurement beam through the test solution; a first fiber optic transmission element operative to transmit the measurement beam from said electromagnetic radiation source to said optical element; a detector operative to measure the intensity of the measurement beam passed through the test solution as a function of the electromagnetic radiation wavelength over the spectral region from 700 to 2500 nm so as to generate an NIR spectrum of the test solution; a second fiber optic transmission element operative to transmit the measurement beam passed through the test solution from said optical element to said detector; and a processor including an algorithm operative to determine the etch rate of the solid in the etching solution by effecting the steps of an analysis method, comprising generating NIR spectra for a plurality of calibration solutions each comprising at least some of the constituents of the etching solution, wherein the constituents include the etchant species and byproducts of the etching process, measuring the etch rates of the solid for the plurality of calibration solutions using a standard procedure, correlating the NIR spectra generated for the plurality of calibration solutions and the etch rates measured by the standard procedure for the plurality of calibration solutions via a chemometric data manipulation to develop a calibration model and a calibration database, generating an NIR spectrum for a sample of the etching solution, and comparing the NIR spectrum generated for the sample of the etching solution with the calibration database to determine the etch rate for the etching solution.
 19. The apparatus of claim 18, wherein the electromagnetic radiation source is further operative to provide a reference beam of the electromagnetic radiation and the intensity of the measurement beam is corrected for fluctuations in the intensity of the electromagnetic radiation provided by the electromagnetic radiation source based on the intensity of the reference beam.
 20. The apparatus of claim 18, wherein the standard procedure for measuring the etch rate of the solid for a calibration solution comprises measuring the thickness of the solid before and after etching the solid in the calibration solution for a predetermined period of time.
 21. The apparatus of claim 18, wherein the solid comprises a material selected from the group consisting of silicon, silicon oxide and silicon nitride, and combinations thereof.
 22. The apparatus of claim 18, wherein the etching solution comprises an aqueous solution comprising at least one etchant species selected from the group consisting of H⁺, HF, F⁻, HF²⁻, SiF₄, H₂SiF₆, SiF₆ ²⁻, OH⁻, H₂O₂, HO²⁻, S₂O₈ ²⁻, SO₄ ²⁻, SO₃ ²⁻, C₂H₃OH₂, C₂H₃OH⁻, C₂H₃O²⁻, Cl⁻, Br⁻, I⁻, NH₄ ⁻, NO₃ ⁻, NO₂ ⁻, N³⁻, and combinations thereof.
 23. The apparatus of claim 18, wherein said processor is further operative to determine the concentration of a chemical constituent of a semiconductor cleaning solution.
 24. The apparatus of claim 23, wherein the semiconductor cleaning solution is an aqueous solution comprising at least one chemical constituent selected from the group consisting of H₂O₂, O₃, NH₄OH, HCl, HF, H₂SO₄, HNO₃, acetic acid, and combinations thereof. 